I had the most current version of the Nook app running on My Fire HD for a while when I first got it (end of December). I didn't give all the functions a workout to see if there might be any kinks, but I was definitely able to register the app and open DRMed B&N content with no issues.

Getting your hands on the app in order to sideload it should be the only hurdle you face to getting it working. And seeing as how it's easily downloaded from 1mobile, that shouldn't be much of a hurdle at all.